Midsphere Radius of Snub Dodecahedron given Total Surface Area Calculator

✖Total Surface Area of Snub Dodecahedron is the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron.ⓘ Total Surface Area of Snub Dodecahedron [TSA]

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✖Midsphere Radius of Snub Dodecahedron is the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Snub Dodecahedron given Total Surface Area [r_m]

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Midsphere Radius of Snub Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
r_m = sqrt(1/(1-0.94315125924))/2*sqrt(TSA/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Midsphere Radius of Snub Dodecahedron - (Measured in Meter) - Midsphere Radius of Snub Dodecahedron is the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere.
Total Surface Area of Snub Dodecahedron - (Measured in Square Meter) - Total Surface Area of Snub Dodecahedron is the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Snub Dodecahedron: 5500 Square Meter --> 5500 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = sqrt(1/(1-0.94315125924))/2*sqrt(TSA/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) --> sqrt(1/(1-0.94315125924))/2*sqrt(5500/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))

Evaluating ... ...

r_m = 20.9160857582834

STEP 3: Convert Result to Output's Unit

20.9160857582834 Meter --> No Conversion Required

FINAL ANSWER

20.9160857582834 ≈ 20.91609 Meter <-- Midsphere Radius of Snub Dodecahedron

(Calculation completed in 00.004 seconds)

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< Midsphere Radius of Snub Dodecahedron Calculators

Midsphere Radius of Snub Dodecahedron given Volume

LaTeX Go Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)

Midsphere Radius of Snub Dodecahedron given Total Surface Area

LaTeX Go Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))

Midsphere Radius of Snub Dodecahedron given Circumsphere Radius

LaTeX Go Midsphere Radius of Snub Dodecahedron = Circumsphere Radius of Snub Dodecahedron/sqrt(2-0.94315125924)

Midsphere Radius of Snub Dodecahedron

LaTeX Go Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*Edge Length of Snub Dodecahedron

Midsphere Radius of Snub Dodecahedron given Total Surface Area Formula

LaTeX Go

What is a Snub Dodecahedron?

In geometry, the Snub Dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal non-prismatic solids constructed by two or more types of regular polygon faces. The Snub Dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices. Each vertex is identical in such a way that, 4 equilateral triangular faces and 1 pentagonal face are joining together at each vertex. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a compound of two Snub Dodecahedra, and the convex hull of both forms is a truncated icosidodecahedron.

How to Calculate Midsphere Radius of Snub Dodecahedron given Total Surface Area?

Midsphere Radius of Snub Dodecahedron given Total Surface Area calculator uses Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) to calculate the Midsphere Radius of Snub Dodecahedron, Midsphere Radius of Snub Dodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Snub Dodecahedron. Midsphere Radius of Snub Dodecahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Snub Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Midsphere Radius of Snub Dodecahedron given Total Surface Area, enter Total Surface Area of Snub Dodecahedron (TSA) and hit the calculate button. Here is how the Midsphere Radius of Snub Dodecahedron given Total Surface Area calculation can be explained with given input values -> 20.91609 = sqrt(1/(1-0.94315125924))/2*sqrt(5500/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))).

FAQ

What is Midsphere Radius of Snub Dodecahedron given Total Surface Area?

Midsphere Radius of Snub Dodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Snub Dodecahedron and is represented as r_m = sqrt(1/(1-0.94315125924))/2*sqrt(TSA/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) or Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))). Total Surface Area of Snub Dodecahedron is the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron.

How to calculate Midsphere Radius of Snub Dodecahedron given Total Surface Area?

Midsphere Radius of Snub Dodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Snub Dodecahedron is calculated using Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))). To calculate Midsphere Radius of Snub Dodecahedron given Total Surface Area, you need Total Surface Area of Snub Dodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Snub Dodecahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Midsphere Radius of Snub Dodecahedron?

In this formula, Midsphere Radius of Snub Dodecahedron uses Total Surface Area of Snub Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*Edge Length of Snub Dodecahedron
Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)
Midsphere Radius of Snub Dodecahedron = Circumsphere Radius of Snub Dodecahedron/sqrt(2-0.94315125924)

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